Derivatives, especially derivatives of forward contracts, are important for risk management and hedging. However there is currently no method available to price contingent claims where the underlying asset is a claim on some part of a network and taking into account properties of forward prices on networks, specifically geographical-(no)-arbitrage and the requirement that tradeable commodities (e.g. Forwards) should be Martingales (under an appropriate measure). Forward derivatives will be of larger importance for bandwidth than for many conventional commodities because bandwidth cannot be stored for later use whilst forward-based contracts are storable over their lifetime (creation to maturity).
A forward contract is a contract entered into at a given time for certain delivery at a later point in time, the contract maturity T. The price of a forward contract is often denoted by F(0,T) when it is entered into and denoted by F(t,T) at later times where t>=0 and t<=T.
A forward curve at any time t is a set of prices of forward contracts of different maturities. For example a forward curve at time t for maturities between t and T* (where T*>=t) comprises all the forward prices F(t,T) with such that T>=t and T<=T*.
Bandwidth is becoming commoditized and markets are starting to appear. Potential behaviors of these markets are not understood because these markets are still in the early stages of development. The instruments traded on bandwidth markets, mostly over-the-counter (OTC), are typically forward contracts covering long (months to years) periods. This is partly due to inefficient negotiation and contract settlement mechanisms. New switching technologies, public pooling, and interconnection points are expected to hasten automation towards more liquid bandwidth markets and shorter contract periods as well as the development of a spot market. Additionally, fiber swaps are not uncommon. Forward derivatives, especially forward call options, are expected to appear given their appropriateness for risk management. Call options on forwards provide the right, but not the obligation, to use capacity in the future starting at some fixed date for a given duration upon payment of some price agreed when the contract is established. These options may be of a European (decide on use only at maturity), American (decide on use at any time up to maturity), or other type (design to meet customer requirements). Swaptions between different network providers are developing together with more specialised instruments with unique applicability to a networked commodity. Point-to-point bandwidth capacity cannot be stored for later use and so forward contracts are the primary market instruments, as in other commodity markets including electricity.
Today, there is no suitable forward curve model that takes into account the special characteristics of bandwidth as a tradable commodity. Standard models cannot be blindly applied because they generate geographical arbitrage opportunities since they do not take into account alternative paths between points with equivalent quality of service (QoS).
Hence a model of the forward curve to price a particular set of forward-derivative contracts will be highly useful both for comparing different forward contracts and for valuing derivatives. A forward contract is defined as a contract in which capacity is bought today to be used starting at a fixed date in the future and for a fixed duration. As indicated, conventional forward curve models developed are insufficient because they do not include the network structure of the bandwidth market. That is, alternative routes with equivalent quality of service (QoS) are perfect substitutes. This has been shown to greatly affect spot price development.
There is a need for a multi-factor forward curve model that takes into consideration geographical arbitrage terms and desired properties such as the Martingale structure. The model should allow the calculation of a distribution of forward prices for using links in a network.
This patent application is related to another patent application, entitled “METHOD AND DEVICE FOR CALCULATING A PRICE FOR USING A SPECIFIC LINK IN A NETWORK” filed on 18 Apr. 2001, presently assigned to the assignee of the instant application and the disclosure of which is incorporated herein by reference.